GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 13 Dec 2018, 00:42

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • The winning strategy for 700+ on the GMAT

     December 13, 2018

     December 13, 2018

     08:00 AM PST

     09:00 AM PST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
  • GMATbuster's Weekly GMAT Quant Quiz, Tomorrow, Saturday at 9 AM PST

     December 14, 2018

     December 14, 2018

     09:00 AM PST

     10:00 AM PST

    10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.

If n is an integer, which of the following must also be an integer?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6625
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
If n is an integer, which of the following must also be an integer?  [#permalink]

Show Tags

New post 18 Jul 2018, 04:04
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

63% (01:16) correct 37% (01:18) wrong based on 138 sessions

HideShow timer Statistics

[GMAT math practice question]

If n is an integer, which of the following must also be an integer?

I. \(\frac{n(n+1)}{2}\)
II. \(\frac{n(n+1)(n+2)}{6}\)
III. \(\frac{n(n+1)(n+2)(n+3)}{8}\)

A. I only
B. II only
C. III only
D. I and II
E. I, II and III

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

MBA Section Director
User avatar
V
Affiliations: GMATClub
Joined: 22 May 2017
Posts: 1425
Concentration: Nonprofit
GPA: 4
WE: Engineering (Computer Software)
If n is an integer, which of the following must also be an integer?  [#permalink]

Show Tags

New post 18 Jul 2018, 06:45
1
I) Since n is an integer, either n or n+1 has to be even. S0, one of n and (n+1) is divisible by 2

\(\frac{n(n+1)}{2}\) is an integer

II) The product of any 3 consecutive integers is divisible by 3

=> one of n, n+1, n+2 is divisible by 3

one of n, n+1, n+2 is also even.

So, \(n(n+1)(n+2)\) is divisible by both 3 and 2 and hence is divisible by 6

\(\frac{n(n+1)(n+2)}{6}\) yields an integer

III) \(n(n+1)(n+2)(n+3)\)

The product of any 4 consecutive integers includes a multiple of 2 and a multiple of 4 provided none of the 4 integers is 0

=> \(n(n+1)(n+2)(n+3)\) is divisible by 8

=> \(\frac{n(n+1)(n+2)(n+3)}{8}\) yields an integer

Hence option E
_________________

New project wSTAT(which Schools To Apply To?)

GMATClub School Ambassador

B-School app with GRE

New - RC Butler - 2 RC's everyday

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6625
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: If n is an integer, which of the following must also be an integer?  [#permalink]

Show Tags

New post 20 Jul 2018, 00:28
=>

Statement I
Since \(n\) and \(n + 1\) are consecutive integers, \(n(n+1)\) is a multiple of \(2\).
Thus, \(\frac{n(n+1)}{2}\) is an integer.

Statement II
Since \(n\) and \(n + 1\) are consecutive integers, \(n(n+1)\) and \(n(n+1)(n+2)\) are multiples of \(2\).
Since \(n, n + 1\) and \(n + 2\) are three consecutive integers, \(n(n+1)(n+2)\) is a multiple of \(3\).
Thus, \(n(n+1)(n+2)\) is a multiple of \(6\), and \(\frac{n(n+1)(n+2)}{6}\) is an integer.

Statement III
Since \(n\) and \(n + 1\) are two consecutive integers, \(n(n+1)\) is a multiple of \(2\).
Similarly, \((n+2)(n+3)\) is a multiple of \(2\).
Also, either n and \(n + 2\) or \(n + 1\) and \(n + 3\) are consecutive even integers. Thus, either \((n + 1)(n+3)\) is a multiple of \(8\) or \(n(n+2)\) is a multiple of \(8\) since one of them is a multiple of \(4\).
It follows that \(n(n+1)(n+2)(n+3)\) is a multiple of \(8\), and \(\frac{n(n+1)(n+2)(n+3)}{8}\) is an integer.

Therefore, the answer is E.

Answer: E
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Manager
Manager
avatar
S
Joined: 05 Feb 2016
Posts: 144
Location: India
Concentration: General Management, Marketing
WE: Information Technology (Computer Software)
GMAT ToolKit User CAT Tests
Re: If n is an integer, which of the following must also be an integer?  [#permalink]

Show Tags

New post 20 Jul 2018, 00:54
1
MathRevolution wrote:
[GMAT math practice question]

If n is an integer, which of the following must also be an integer?

I. \(\frac{n(n+1)}{2}\)
II. \(\frac{n(n+1)(n+2)}{6}\)
III. \(\frac{n(n+1)(n+2)(n+3)}{8}\)

A. I only
B. II only
C. III only
D. I and II
E. I, II and III


From1: n,n+1 is product of two consecutive integer so divisible by 2 :sufficient
From2: n,n+1,n+2 is product of three consecutive integer so divisible by 2 and 3 :sufficient
From1: n,n+1,n+2,n+3 is product of four consecutive integer so divisible by 8
Intern
Intern
avatar
B
Joined: 06 May 2018
Posts: 2
Re: If n is an integer, which of the following must also be an integer?  [#permalink]

Show Tags

New post 24 Jul 2018, 11:09
1
Quote:
If n is an integer, which of the following must also be an integer?


Is the question stem supposed to say "If n is a positive integer?"
Senior Manager
Senior Manager
User avatar
P
Joined: 04 Jun 2018
Posts: 358
Location: Germany
Concentration: General Management, Finance
GPA: 3.6
WE: Analyst (Transportation)
Premium Member Reviews Badge CAT Tests
Re: If n is an integer, which of the following must also be an integer?  [#permalink]

Show Tags

New post 24 Jul 2018, 11:44
1
blackshadow1357 wrote:
Quote:
If n is an integer, which of the following must also be an integer?


Is the question stem supposed to say "If n is a positive integer?"


I had the same thougt, if n= -1 then n+1 is 0 and thus 1*0 / 2 is not an integer.
_________________

A couple of things that helped me in verbal:
https://gmatclub.com/forum/verbal-strategies-268700.html#p2082192

Gmat Prep CAT #1: V42, Q34, 630
Gmat Prep CAT #2: V46, Q35, 660
Gmat Prep CAT #3: V41, Q42, 680

On the mission to improve my quant score, all help is appreciated! :)

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6625
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: If n is an integer, which of the following must also be an integer?  [#permalink]

Show Tags

New post 30 Jul 2018, 07:45
blackshadow1357 wrote:
Quote:
If n is an integer, which of the following must also be an integer?


Is the question stem supposed to say "If n is a positive integer?"


We don't need the assumption n is a positive integer.
It is valid for 0 or negative integers too.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6625
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: If n is an integer, which of the following must also be an integer?  [#permalink]

Show Tags

New post 30 Jul 2018, 07:46
Arro44 wrote:
blackshadow1357 wrote:
Quote:
If n is an integer, which of the following must also be an integer?


Is the question stem supposed to say "If n is a positive integer?"


I had the same thougt, if n= -1 then n+1 is 0 and thus 1*0 / 2 is not an integer.


1*0 / 2 = 0 is an integer.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

GMAT Club Bot
Re: If n is an integer, which of the following must also be an integer? &nbs [#permalink] 30 Jul 2018, 07:46
Display posts from previous: Sort by

If n is an integer, which of the following must also be an integer?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.